First slide

Combinations

Question

Team ‘A’ consists of 7 boys and n girls and Team ‘B’ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to

Moderate

A

4
B

5
C

6
D

7

Solution

$7_{C_{1}} . 4_{C_{1}} + n_{C_{1}} . 6_{C_{1}} = 52 \Rightarrow 28 + 6 n = 52 \Rightarrow 6 n = 24 \Rightarrow n = 4$

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